Re: [M&M 2nd ed] How would you build this character?
So, kindof like the ships in the series Andromeda, where the ship has an AI, and also a robotic avatar for going around places? There's a couple ways I could see to do that, but it depends on whether they will primarily act through the avatar, or essentially be like riggers in Shadowrun, and have a series of drones he can send out.
If you're primarily going through a single avatar, then build the avatar like any other character, but making it a Construct (CON --, appropriate immunities, etc.), with whatever powers you deemed appropriate. If they want the ability to swap out abilities depending on the situation, then I would put it as either an array or a variable power structure, depending on taste, limited so that it takes time in a shop to change it. Build the headquarters with equipment points, and you're golden.
If you're doing the AI rigger route, then build the character like you would an AI. Have a -- in all physical attributes, and build the headquarters as a base. Then use powers like Datalink, Summon, Possession (limited to Machines), Mind Control (limited to machines), Animate Object, and so on to do powers. Datalink allows you to get into any computers around. Summon works best for robot constructs and such. If you want more variety in the constructs, consider doing alternate powers on the Summon, though if you want to have a single, more powerful avatar that can work alongside the minions, I'd make that a separate summon power, so you can run them side-by-side. Possession limited to machines allows you to jump into that tank someone brought to the party and BE the tank. Mind control limited to machines will let you 'hack' other machine intelligences (and can also be used to counter the power if it is used against you). Animate Object (limited to machines) allows you to control mechanical doors, control the security system, and so on.